{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TG5W3R3GTYYAUM7DXUQH3XBWUR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"af8328cf2d061caa018b3f6b1c34d2fb2ac3ffb0eba2101d909bf9913df2d7fe","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-13T17:43:09Z","title_canon_sha256":"44352b23fb08d322d86f71f31d54eee5f3cfb13d69df346071587b053aca76bb"},"schema_version":"1.0","source":{"id":"2608.13523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13523","created_at":"2026-08-14T01:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13523v1","created_at":"2026-08-14T01:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13523","created_at":"2026-08-14T01:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"TG5W3R3GTYYA","created_at":"2026-08-14T01:24:57Z"},{"alias_kind":"pith_short_16","alias_value":"TG5W3R3GTYYAUM7D","created_at":"2026-08-14T01:24:57Z"},{"alias_kind":"pith_short_8","alias_value":"TG5W3R3G","created_at":"2026-08-14T01:24:57Z"}],"graph_snapshots":[{"event_id":"sha256:db93c6e4cdca9450610f8334837bdbe4c8171c429335ab4f14ba12414d2ee344","target":"graph","created_at":"2026-08-14T01:24:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.13523/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a Polish space and let $\\mathcal K(X)$ be its Vietoris hyperspace. A family $\\mathcal I\\subseteq\\mathcal K(X)$ is hereditary if it is downward closed under inclusion. Matheron and Zelen\\'y asked whether every comeager hereditary family in $\\mathcal K(X)$ contains a dense hereditary $G_\\delta$ subfamily. We give an affirmative answer in ZFC.","authors_text":"Peter Ban\\'a\\v{s}","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-13T17:43:09Z","title":"Comeager hereditary families of compact sets are big"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13523","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:49a8acd3a0c571773ca9d657f8c5e0b8d6eef23b2d46900c8e138e34a4534d4e","target":"record","created_at":"2026-08-14T01:24:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"af8328cf2d061caa018b3f6b1c34d2fb2ac3ffb0eba2101d909bf9913df2d7fe","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-08-13T17:43:09Z","title_canon_sha256":"44352b23fb08d322d86f71f31d54eee5f3cfb13d69df346071587b053aca76bb"},"schema_version":"1.0","source":{"id":"2608.13523","kind":"arxiv","version":1}},"canonical_sha256":"99bb6dc7669e300a33e3bd207ddc36a4714474c88831eb8d5d93f20e0f1c9457","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99bb6dc7669e300a33e3bd207ddc36a4714474c88831eb8d5d93f20e0f1c9457","first_computed_at":"2026-08-14T01:24:57.562755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:24:57.562755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6y6Chg/Z31uQO03gwjB1uz+k2F0FaL9djbUCV2d5Cwm+uZ3IcnftrdK7nhBcC3i02gw+rQ6gOgJENx08Ej82Ag==","signature_status":"signed_v1","signed_at":"2026-08-14T01:24:57.564930Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49a8acd3a0c571773ca9d657f8c5e0b8d6eef23b2d46900c8e138e34a4534d4e","sha256:db93c6e4cdca9450610f8334837bdbe4c8171c429335ab4f14ba12414d2ee344"],"state_sha256":"d40705640c177c032b53a314ee1a2a5a77365877eb1479ede7af53f53ed2f269"}